Micro-electro-mechanical system (MEMS) variable capacitor apparatuses, systems and related methods

ABSTRACT

Micro-electro-mechanical system (MEMS) variable capacitor apparatuses, system and related methods are provided.

RELATED APPLICATION

[0001] This application claims the benefit of U.S. Provisional PatentApplication Serial No. 60/433,454, filed Dec. 13, 2002; the disclosureof which is incorporated herein by reference in its entirety.

[0002] Additionally, co-pending U.S. patent application Ser. No.10/461,021, filed Jun. 13, 2003, entitled “Micro-Electro-MechanicalSystem (MEMS) Variable Capacitor Apparatuses and Related Methods”, isincorporated herein by reference in its entirety.

TECHNICAL FIELD

[0003] The present subject matter relates generally tomicro-electro-mechanical systems (MEMS) apparatuses and methods. Moreparticularly, the present subject matter relates to variable capacitorapparatuses and related methods utilizing MEMS technology.

BACKGROUND ART

[0004] Micro-electro-mechanical systems (MEMS) apparatuses and methodsare presently being developed for a wide variety of applications in viewof the size, cost and power consumption advantages provided by thesedevices. Specifically, a variable capacitor, also known as a varactor,can be fabricated utilizing MEMS technology. Typically, a variablecapacitor includes an interelectrode spacing (or an electrode overlaparea) between a pair of electrodes that can be controllably varied inorder to selectively vary the capacitance between the electrodes. Inthis regard, conventional MEMS variable capacitors include a pair ofelectrodes, one that is typically disposed upon and fixed to thesubstrate and the other that is typically carried on a movable actuatoror driver. In accordance with MEMS technology, the movable actuator istypically formed by micromachining the substrate such that very smalland very precisely defined actuators can be constructed.

[0005] As appreciated by persons skilled in the art, many types of MEMSvariable capacitors and related devices can be fabricated by either bulkor surface micromachining techniques. Bulk micromachining generallyinvolves sculpting one or more sides of a substrate to form desiredthree dimensional structures and devices in the same substrate material.The substrate is composed of a material that is readily available inbulk form, and thus ordinarily is silicon or glass. Wet and/or dryetching techniques are employed in association with etch masks and etchstops to form the microstructures. Etching is typically performedthrough the backside of the substrate. The etching technique cangenerally be either isotropic or anisotropic in nature. Isotropicetching is insensitive to the crystal orientation of the planes of thematerial being etched (e.g., the etching of silicon by using a nitricacid as the etchant). Anisotropic etchants, such as potassium hydroxide(KOH), tetramethyl ammonium hydroxide (TMAH), and ethylenediaminepyrochatechol (EDP), selectively attack different crystallographicorientations at different rates, and thus can be used to definerelatively accurate sidewalls in the etch pits being created. Etch masksand etch stops are used to prevent predetermined regions of thesubstrate from being etched.

[0006] On the other hand, surface micromachining generally involvesforming three-dimensional structures by depositing a number of differentthin films on the top of a silicon wafer, but without sculpting thewafer itself. The films usually serve as either structural orsacrificial layers. Structural layers are frequently composed ofpolysilicon, silicon nitride, silicon dioxide, silicon carbide, oraluminum. Sacrificial layers are frequently composed of polysilicon,photoresist material, polimide, metals, or various types of oxides, suchas PSG (phosphosilicate glass) and LTO (low-temperautre oxide).Successive deposition, etching, and patterning procedures are carriedout to arrive at the desired microstructure. In a typical surfacemicromachining process, a silicon substrate is coated with an isolationlayer, and a sacrificial layer is deposited on the coated substrate.Windows are opened in the sacrificial layer, and a structural layer isthen deposited and etched. The sacrificial layer is then selectivelyetched to form a free-standing, movable microstructure such as a beam ora cantilever out of the structural layer. The microstructure isordinarily anchored to the silicon substrate, and can be designed to bemovable in response to an input from an appropriate actuating mechanism.

[0007] MEMS variable capacitors have been fabricated that include amovable, capacitive plate (or electrode) that is suspended above firstand second coplanar electrodes. The variable capacitor operates byapplying a voltage across the first electrode and the movable plate sothat the plate is deflected towards the first electrode by electrostaticattraction. As the movable plate moves, the spacing between the secondelectrode and the movable plate changes, thus changing the capacitancevalue between the second electrode and the plate. A signal line isusually connected to the second electrode and the plate to sense thechange in capacitance for use in various Radio Frequency functions. Oneproblem with this configuration is that the voltage supply iselectrically connected to the signal line through the plate that canresult in undesirable noise/interference or degradation of the signal onthe signal line. Thus, this configuration may require additionalcomponents to combine/separate the signal and actuation voltage, leadingto a more complex and costly implementation. Another problem is that theRF voltage exerts an equivalent force on the movable plate to thatexerted by the intended control voltage, leading to control complexityand increased intermodulation.

[0008] Other known MEMS variable capacitors provide parallel-plateelectrodes that move linearly. The electrodes of these variablecapacitors are subject to suddenly “snapping down” towards one anotherafter moving close enough to one another. These types of variablecapacitors are also subject to microphonics and stiction problems.

[0009] Some MEMS variable capacitors are based upon electro-thermallyactuated parallel-plate design. These types of variable capacitors aresubject to reduced power handling capability due to gap reduction andthe likelihood for breakdown occurrence. These variable capacitors alsoconsume excessive power, especially if the electro-thermal actuationmust be applied continuously to maintain the capacitance value.

[0010] Other MEMS variable capacitors utilize a massively-parallel,interdigited-comb device for actuation. These variable capacitors are sosensitive to parasitic substrate capacitance that they require either ahigh-resistivity substrate such as glass or the removal of the substratebeneath the MEMS device. Thus, this type of variable capacitor is notreadily integrated into a conventional integrated circuit (IC) process.Additionally, the MEMS device is physically large because thecapacitance dependence on the overlap of comb fingers requires largeaspect ratios. These devices require excessive space and cause a lowresonant frequency resulting in shock and vibration problems.

[0011] Therefore, it is desirable to provide novel variable capacitorapparatuses and related methods for MEMS applications that improve uponaforementioned designs.

SUMMARY

[0012] It is an object to provide a MEMS variable capacitor forelectrically isolating the capacitive and actuation plates. It is alsoan object to provide a MEMS variable capacitor for reducingelectrostatic instability. Further, it is an object to at leastpartially mechanically decouple the movable capacitive and actuationplates of a MEMS variable capacitor. It is therefore an object toprovide novel MEMS variable capacitor apparatuses and related methods.

[0013] Some of the objects of the present disclosure having been statedhereinabove, and which are addressed in whole or in part by the presentdisclosure, other objects will become evident as the descriptionproceeds when taken in connection with the accompanying drawings as bestdescribed hereinbelow.

BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Exemplary embodiments will now be explained with reference to theaccompanying drawings, of which:

[0015]FIG. 1 is a top view of an exemplary MEMS variable capacitor;

[0016]FIG. 2A is a cross-section side view of one embodiment of thevariable capacitor shown in FIG. 1;

[0017]FIG. 2B is a cross-section side view of an alternative embodimentof the variable capacitor shown in FIG. 1;

[0018]FIG. 2C is a cross-section side view of another alternativeembodiment of the variable capacitor shown in FIG. 1;

[0019]FIG. 3 is a cross-sectional side view of the variable capacitorshown in FIG. 2A with the voltage applied to a movable actuationelectrode and a stationary actuation electrode set greater than 0 Volts;

[0020]FIG. 4 is a top perspective view of a variable capacitor includinga movable component suspended above a substrate;

[0021]FIG. 5 is a cross-sectional side view of the variable capacitorshown in FIG. 4;

[0022]FIG. 6 is another cross-sectional side view of the variablecapacitor shown in FIG. 4;

[0023]FIG. 7 is a top view of variable capacitor shown in FIG. 4;

[0024]FIG. 8 is a top perspective view of the variable capacitor shownin FIG. 4 with the voltage applied to the actuation electrodes set to avoltage greater than 0 Volts for overcoming the resistive force oftethers;

[0025]FIG. 9 is a computer simulation model of the z-displacement of amovable component at its first resonance mode;

[0026]FIG. 10 is a computer simulation model of the z-displacement of amovable component versus actuation voltage;

[0027]FIG. 11 is a computer simulation model of the z-displacement ofmovable component for an actuation voltage of about 25 Volts;

[0028]FIG. 12 is a graph showing capacitance (pF) between stationarycapacitive electrode and movable capacitive electrodes versus voltageapplied to electrodes shown in FIG. 5;

[0029]FIG. 13A is a computer simulation model of the deformation ofmovable component for a residual stress value of 120 MPa;

[0030]FIG. 13B is a computer simulation model of deformation of amovable component under a stress gradient between +10 and −10 MPa;

[0031]FIG. 14 is a computer simulation model of an equivalent circuit ofthe variable capacitor shown in FIG. 4;

[0032]FIGS. 15A, 15B, and 15C are computer simulation models ofdeformation of movable component under a stress gradient between +10 and−10 MPa;

[0033]FIG. 16 is a computer simulation model of an exemplaryelliptically-shaped interior portion with the same area under the samestress gradients;

[0034]FIG. 17 is a computer simulation model of the deformation of aninterior portion for an acceleration of 100 g;

[0035]FIG. 18 is a graph showing different tether lengths and peripheralportion widths versus actuation voltage for a variable capacitor;

[0036]FIG. 19 is a graph showing different tether lengths and peripheralportion widths versus resonance frequency for a variable capacitor;

[0037]FIG. 20 is a computer simulation model of the z-displacement ofthe first resonance mode of a variable capacitor having a tether lengthof 75 micrometers and peripheral portion width of 75 micrometers;

[0038]FIG. 21 is a computer simulation model of the z-displacement of avariable capacitor having a tether length of 75 micrometers andperipheral portion width of 75 micrometers at an actuation voltage setat 14 Volts;

[0039]FIG. 22 is a graph showing displacement of the center of avariable capacitor having a tether length of 75 micrometers andperipheral portion width of 75 micrometers versus voltage applied to theactuation electrodes;

[0040]FIG. 23 is a computer simulation model of the z-displacement of aninterior portion of a variable capacitor exposed to a temperaturedifference;

[0041]FIG. 24 is another computer simulation model of the z-displacementof an interior portion of a variable capacitor exposed to a temperaturedifference;

[0042]FIG. 25 is a computer simulation model of the deformation of aninterior component having a tether length of 75 micrometers andperipheral portion width of 75 micrometers for an acceleration of 100 g;

[0043]FIG. 26 is a top perspective view of another exemplary variablecapacitor;

[0044]FIG. 27A is a cross-sectional side view of one aperture;

[0045]FIG. 27B is a cross-sectional side view of another aperture;

[0046]FIG. 28 is a graph showing the cut-off frequency of a variablecapacitor versus the number of apertures in an interior portion of thevariable capacitor;

[0047]FIG. 29 is a graph showing the damping and tether forces versusfrequency for different number of apertures;

[0048]FIG. 30 is a graph showing the damping coefficient as a functionof the frequency for different numbers of apertures;

[0049]FIG. 31 is a graph showing harmonic analysis of a variablecapacitor having an interior portion with 37 apertures;

[0050]FIG. 32 is a graph showing the cut-off frequency for differentaperture numbers;

[0051]FIG. 33 is a graph showing the effective area of the capacitiveelectrode as a function of the number of apertures for four differentcases according to the minimum distance between the gold layer and theopening of an interior portion;

[0052]FIG. 34 is a top view of exemplary cascade arrangement of aplurality of variable capacitors;

[0053]FIG. 35 is a top view of exemplary cascade of plurality ofvariable capacitors in a fanned-shape arrangement;

[0054]FIG. 36A is a computer simulation model for an equivalent circuitof four variable capacitors arranged in parallel;

[0055]FIG. 36B is the RF results of the computer simulation shown inFIG. 36B;

[0056]FIG. 37A is a top perspective view of another exemplary variablecapacitor utilizing a rectangular geometry including a suspended,movable component;

[0057]FIG. 37B is a top perspective view of another exemplary variablecapacitor including a suspended, movable component;

[0058]FIG. 38 is a cross-sectional side view of a variable capacitorhaving isolation bumps;

[0059]FIG. 39 is a cross-sectional side view of the variable capacitorshown in FIG. 38 when actuation voltage has been applied to theactuation electrodes;

[0060]FIG. 40 is a cross-sectional side view of another variablecapacitor having an isolation bump;

[0061]FIG. 41 is a cross-sectional side view of another variablecapacitor having an isolation bump;

[0062]FIG. 42 is cross-sectional side view of another variable capacitorhaving isolation bumps;

[0063]FIG. 43 is a top perspective view of variable capacitor;

[0064]FIG. 44A is a cross-sectional side view of the variable capacitorshown in FIG. 43;

[0065]FIG. 44B is a cross-sectional side view of an alternativeembodiment of the variable capacitor shown in FIG. 43;

[0066]FIG. 45 is a cross-sectional side view of variable capacitor in anactuated mode;

[0067]FIG. 46 is a graph showing the harmonic behavior for variablecapacitor;

[0068]FIG. 47 is a graph showing the frequency response for differentdistances of the movable actuation electrodes and the movable capacitiveelectrodes shown in FIG. 43;

[0069]FIG. 48 is a top view of a schematic diagram of another examplarytorsional variable capacitor;

[0070]FIG. 49 is a computer simulation model of deformation of atorsional variable capacitor of an array of 16 variable capacitors;

[0071]FIG. 50 is a graph showing the capacitance of a torsional variablecapacitor versus an applied actuation voltage;

[0072]FIG. 51 is a computer simulation model of deformation of a movablecomponent of a torsional variable capacitor under a stress gradientbetween +1 and −1 MPa;

[0073]FIG. 52 is a computer simulation model of the deformation of amovable component in a torsional variable capacitor for an accelerationof 100 g;

[0074]FIG. 53A is a computer simulation model for an equivalent circuitof a torsional variable capacitor; and

[0075]FIG. 53B is the RF results of the computer simulation model shownin FIG. 53A.

DETAILED DESCRIPTION

[0076] It is understood that when a component such as a layer,substrate, contact, interconnect, electrode, capacitive plate, orconductive line is referred to herein as being deposited or formed “on”another component, that component can be directly on the other componentor, alternatively, intervening components (for example, one or morebuffer or transition layers, interlayers, electrodes or contacts) canalso be present. Furthermore, it is understood that the terms “disposedon”, “attached to” and “formed on” are used interchangeably to describehow a given component is positioned or situated in relation to anothercomponent. Therefore, it will be understood that the terms “disposedon”, “attached to” and “formed on” do not introduce any limitationsrelating to particular methods of material transport, deposition, orfabrication.

[0077] Contacts, interconnects, electrodes, capacitive plates,conductive lines, and other various conductive elements of variousmetals can be formed by sputtering, CVD, or evaporation. If gold,copper, nickel or Permalloy™ (Ni_(x)Fe_(y)) is employed as the metalelement, an electroplating process can be carried out to transport thematerial to a desired surface. The chemical solutions used in theelectroplating of various metals are generally known. Some metals, suchas gold, might require an appropriate intermediate adhesion layer toprevent peeling. Examples of adhesion material often used includechromium, titanium, or an alloy such as titanium-tungsten (TiW). Somemetal combinations can require a diffusion barrier to prevent a chromiumadhesion layer from diffusing through gold. Examples of diffusionbarriers between gold and chromium would include platinum or nickel.

[0078] Conventional lithographic techniques can be employed inaccordance with micromachining of the variable capacitors. Accordingly,basic lithographic process steps such as photoresist application,optical exposure, and the use of developers are not described in detailherein.

[0079] Similarly, generally known-etching processes can be employed toselectively remove material or regions of material. An imagedphotoresist layer is ordinarily used as a masking template. A patterncan be etched directly into the bulk of a substrate, or into a thin filmor layer that is then used as a mask for subsequent etching steps.

[0080] The type of etching process employed in a particular fabricationstep (e.g., wet, dry, isotropic, anisotropic, anisotropic-orientationdependent), the etch rate, and the type of etchant used will depend onthe composition of material to be removed, the composition of anymasking or etch-stop layer to be used, and the profile of the etchedregion to be formed. As examples, poly-etch (HF:HNO ₃:CH₃COOH) cangenerally be used for isotropic wet etching. Hydroxides of alkali metals(e.g., KOH), simple ammonium hydroxide (NH₄OH), quaternary (tetramethl)ammonium hydroxide ((CH₃)₄ NOH, also known commercially as TMAH), andethylenediamine mixed with pyrochatechol in water (EDP) can be used foranisotropic wet etching to fabricate V-shaped or tapered grooves,trenches or cavities. Silicon nitride is typically used as the maskingmaterial against ethcing by KOH, and thus can be used in conjunctionwith the selective etching of silicon. Silicon dioxide is slowly etchedby KOH, and thus can be used as a masking layer if the etch time isshort. While KOH will etch undoped silicon, heavily doped (p++) siliconcan be used as an etch-stop against KOH as well as the alkaline etchantsand EDP. The preferred metal used to form contacts and interconnects isgold, which is resistant to EDP. The adhesion layer applied inconnection with forming a gold component (e.g., chromium) is alsoresistant to EDP.

[0081] It will be appreciated that electrochemical etching in hydroxidesolution can be performed instead of timed wet etching. For example, ifa p-type silicon wafer is used as a substrate, an etch-stop can becreated by epitaxially growing an n-type silicon end layer to form a p-njunction diode. A voltage is applied between the n-type layer and anelectrode disposed in the solution to reverse-bias the p-n junction. Asa result, the bulk p-type silicon is etched through a mask down to thep-n junction, stopping at the n-type layer. Furthermore, photovoltaicand galvanic etch-stop techniques are also suitable.

[0082] Dry etching techniques such as plasma-phase etching and reactiveion etching (RIE) can also be used to remove silicon and its oxides andnitrides, as well as various metals. Deep reactive ion etching (DRIE)can be used to anisotropically etch deep, vertical trenches in bulklayers. Silicon dioxide is typically used as an etch-stop against DRIE,and thus structures containing a buried silicon dioxide layer, such assilicon-on-insulator (SOI) wafers, can be used as starting substratesfor the fabrication of microstructures.

[0083] An alternative patterning process to etching is the lift-offprocess. In this case, the conventional photolithography techniques areused for the negative image of the desired pattern. This process istypically used to pattern metals, which are deposited as a continuousfilm or films when adhesion layers and diffusion barriers are needed.The metal is deposited on the regions where it is to be patterned and ontop of the photoresist mask (negative image). The photoresist and metalon top are removed to leave behind the desired pattern of metal.

[0084] As used herein, the term “device” is interpreted to have ameaning interchangeable with the term “component”.

[0085] As used herein, the term “conductive” is generally taken toencompass both conducting and semi-conducting materials. Examples of themethods of the present subject matter will now be described withreference to the accompanying drawings.

[0086] Referring to FIGS. 1-3, different views of an exemplary MEMSvariable capacitor, generally designated 100, are illustrated. FIG. 1illustrates a top view of variable capacitor 100 including a movablecomponent MC suspended over a substrate (designated 200 in FIG. 2A).Movable component MC can include a movable actuation electrode MAE and amovable capacitive electrode MCE disposed on a top surface thereof.Alternatively, movable actuation electrode MAE and a movable capacitiveelectrode MCE can be connected to a bottom surface of movable componentMC or the top and bottom surfaces can each include a movable actuationelectrode and a movable capacitive electrode. Additionally, one ofmovable actuation electrode MAE and a movable capacitive electrode MCEcan be a completely conducting section of movable component MC ratherthan a layer. Movable component MC can comprise one or more layers ofsilica, alumina, un-doped semiconductors, polymers, and othernon-conductive materials known to those of skill in the art. Thematerial of movable component MC can function to electrically isolateactuation electrode MAE from capacitive electrode MCE and provideflexibility for deflecting.

[0087] Movable component MC can include a plurality of tethers T1, T2,T3, and T4 connected to movable component MC for attaching movablecomponent MC to posts (shown in FIG. 2A) or other suitable supportstructures, which may be the structural layer of movable component MCwith a step formed by the edge of the sacrificial layer duringfabrication. If the process is planarized, the support can be the whole“field” where the top surface is nearly planar. Posts P1 and P2 can berigidly attached to a surface S of substrate 200 (shown in FIG. 2A). Inthis embodiment, tethers T1, T2, T3, and T4 extend along an at leastsubstantially straight line that can be at least substantiallyperpendicular to a line extending from a center C of movable componentMC to the connection of tether T1 to movable component MC. For example,tether T1 extends along broken line 102. Broken line 104 extends fromcenter C to the point of attachment for tether T1 and movable componentMC. Broken lines 102 and 104 are at least substantially perpendicular.Alternatively, broken lines 102 and 104 can be at other suitable angleswith respect to one another. Tethers T1, T2, T3, and T4 can function asstress decouplers, in order to reduce the effects of in-plane stressessuch as residual stress, mounting stress and thermal expansion mismatchstress. Additionally, tethers T1, T2, T3, and T4 can reduce the impactof the gradient of the out-of-plane distribution of these in-planestresses. Tethers T1, T2, T3, and T4 can also reduce the impact of theaverage of the out-of-plane distribution. This results in makingvariable capacitor 100 less sensitive to process tolerances related tostress control. A voltage supply and signal line can be used to connectmovable actuation electrode MAE and movable capacitive electrode MCE asshown with reference to subsequent figures.

[0088]FIG. 2A illustrates a cross-sectional side view of one embodimentof variable capacitor 100. Variable capacitor 100 can include substrate200 comprising one or more layers, composites, or other combinations ofsilicon, alumina, silica, polymers and other suitable substratematerials known to those of ordinary skill in the art. A stationaryactuation electrode SAE can be formed on surface 104 of substrate andpositioned directly beneath movable actuation electrode MAE. ElectrodesSAE and MAE can be connected to a voltage supply VS via conductive lines106 and 108, respectively. Voltage supply VS can apply a voltage acrosselectrodes SAE and MAE. An equal and opposite electrical charge developson electrodes SAE and MAE upon the application of a voltage. The equaland opposite electrical charge causes an electrostatic force to pullmovable actuation electrode MAE, and movable component MC, towardsstationary actuation electrode SAE in a direction indicated by directionarrow 110. Tethers T1, T2, T3, and T4 can produce a biasing force tooppose movement of movable component MC in direction indicated by arrow110. Movable component MC can move towards substrate 200 only when thevoltage applied across electrodes SAE and MAE is great enough toovercome the resistive force of tethers T1, T2, T3, and T4. The voltageapplied across electrodes SAE and MAE can be increased to deflectelectrode MAE closer to electrode SAE than another position. Thus, thegap distance between electrodes SAE and MAE can be adjusted bycontrolling the voltage output by voltage supply VS. The voltage appliedby voltage supply VS can be varied directly by an operator or othersuitable electrical circuitry known to those of skill in the art forcontrolling the voltage output by a voltage supply. Movable component MCis shown in position when the voltage applied by voltage supply VS is 0volts.

[0089] Variable capacitor 100 can also include a stationary capacitiveelectrode SCE attached to a base portion 112 disposed on substrate 200.Stationary capacitive electrode SCE can be positioned closer to movablecomponent MC than stationary actuation electrode SAE, spaced apartvertically from stationary actuation electrode SAE, and immediatelyabove base portion 112. Electrode SCE can be positioned directly belowelectrode MCE. Electrodes SCE and MCE can be electrically connected to asignal line SL for supplying a signal, typically AC, to variablecapacitor VC from other electrical circuitry (not shown). Signal line SLcan comprise of a highly-conductive metal such as gold, aluminum,silver, copper, or the like. Signal line SL can be connected to ahigh-frequency distribution network with minimum fixed capacitance.Typically, the electrical circuitry connected to signal line SL issensitive to capacitance of variable capacitor 100. Capacitiveelectrodes MCE and SCE can be moved to different positions with respectto one another when voltage is applied to actuation electrodes MAE andSAE for moving movable component MC. Capacitive electrodes SCE and MCEand actuation electrodes SAE and MAE can comprise any suitable type ofmetal, semi-metal, or doped semiconductor. Capacitive electrodes SCE andMCE can comprise a highly conductive metal, such as copper, gold,silver, aluminum, or the like.

[0090]FIG. 2B illustrates a cross-sectional side view of an alternativeembodiment of variable capacitor 100. In this embodiment, movablecomponent MC comprises a first portion 200 and a second portion 202,wherein second portion 202 is positioned closer to substrate 102 thanfirst portion 200. Therefore, movable actuation electrode MAE andstationary actuation electrode SAE can be positioned further apart thanthe distance between movable capacitance electrode MCE and stationarycapacitance electrode SCE to its attachment to first portion 200 becausemovable actuation electrode MAE is positioned on raised first portion200. The dual gap can be formed by two different thicknesses ofsacrificial layer.

[0091]FIG. 2C illustrates a cross-sectional side view of anotheralternative embodiment of variable capacitor 100. In this embodiment,stationary actuation electrode SAE is buried in substrate 102.Therefore, movable actuation electrode MAE and stationary actuationelectrode SAE can be positioned further apart than the distance betweenmovable capacitance electrode MCE and stationary capacitance electrodeSCE to its attachment to first portion 200 because stationary actuationelectrode SCE is buried in substrate 102. The dual gap can be formed bytwo different thicknesses of sacrificial layer.

[0092] Additionally, in another alternative of FIG. 2B, stationarycapacitive electrode SCE can be positioned parallel with stationaryactuation electrode SAE on substrate 102 such that electrode SCE and SAEare not in electrical communication. In this embodiment, the distancebetween capacitive electrodes MCE and SCE can be about 0.5 micrometers.Additionally, the distance between actuation electrodes MAE and SAE canbe about 2.0 micrometers.

[0093] Referring to FIG. 2C illustrates a cross-sectional side view ofanother alternative embodiment of variable capacitor 100. In thisembodiment, stationary actuation electrode SAE is attached directly ontothe top surface of substrate 102. Stationary actuation electrode SAE canbe buried in substrate 102. This positioning can increase the distancebetween stationary actuation electrode SAE and movable actuationelectrode MAE without adding the complexity of additional sacrificiallayers. Substrate 102 can comprise a dielectric or other suitablesubstrate material.

[0094]FIG. 3 illustrates a cross-sectional side view of the embodimentof variable capacitor 100 shown in FIG. 2A with the voltage applied toelectrodes MAE and SAE set greater than 0 Volts. With the appliedvoltage set greater than 0 Volts, movable component MC can be positionedcloser to substrate 200 than when the applied voltage is set to 0 (asshown in FIG. 2).

[0095] Referring to FIGS. 4-8, different views of an exemplaryhexagonal-shaped implementation of a variable capacitor, generallydesignated 400, are illustrated. FIG. 4 illustrates a top perspectiveview of variable capacitor 400 including a movable component MCsuspended above a substrate 402. Movable component MC can includemovable actuation electrodes MAE1 and MAE2 and a movable capacitiveelectrode MCE1 attached to a top surface 404 of movable component MC.

[0096] Referring to FIG. 4, movable component MC can include aperipheral portion 406 and an interior portion 408. In this embodiment,peripheral portion 406 is hexagonal in shape with a hollow interior forenclosing interior portion 408. Interior portion 408 can be attached toperipheral portion 406 with connectors 410 and 412. There should be atleast two connectors according to this embodiment. The exact number ofconnectors in alternative embodiments can depend on the geometry anddesign rules of a specific design and process. Peripheral portion 406can be attached to substrate 402 via a plurality of tethers T1, T2, T3,T4, T5, and T6. Tethers T1, T2, T3, T4, T5, and T6 can include ends 414,416, 418, 420, 422, and 424, respectively, attached to posts (shown inFIG. 5). The posts or other support structures can be rigidly attachedto substrate 402.

[0097]FIG. 5 illustrates a cross-sectional side view of variablecapacitor 400. Variable capacitor 400 can include posts P1 and P2 orother suitable support structures for attachment to tethers T3 and T6,respectively. Tethers T1, T2, T4, and T5 (shown in FIG. 4) can also beattached to posts (not shown) such as posts P1 and P2 for attachment tosubstrate 402. Movable component MC can also include movable actuationelectrodes MAE3 and MAE4 attached to bottom surface 500 and opposingelectrodes MAE1 and MAE2, respectively. Movable component MC can alsoinclude a movable capacitive electrode MCE2 attached to bottom surface500 and opposing electrode MCE1. Additionally, a movable actuationelectrode (such as movable actuation electrode MAE3) can be positionedon movable component MC directly opposing movable capacitive electrodeMCE1. Electrodes MAE1 and MAE3 can be in electrical communication via aconductive interconnect CI1 extending through movable component MC.Electrodes MAE2 and MAE4 can be in electrical communication via aconductive interconnect CI2 extending through movable component MC.Electrodes MCE1 and MCE2 can be in electrical communication via aconductive interconnect CI3 extending through movable component MC.Electrodes MAE1, MAE2, MAE3, MAE4, MCE1, MCE2 can comprise the sameconductive material and be matched in shape and dimension to itsopposing counterpart on movable component MC for mechanical stressmatching of interior portion 408 (FIG. 4) of movable component MC.Alternatively, electrodes MAE1, MAE2, MAE3, MAE4, MCE1, MCE2 can havedifferent suitable shapes and comprise different materials for providingdesired stress matching.

[0098] Variable capacitor 400 can also include stationary actuationelectrodes SAE1 and SAE2 positioned on the top surface of substrate 402and beneath movable actuation electrodes MAE1 and MAE2, respectively.Alternatively, movable actuation electrodes MAE1 and MAE2 can comprise asingle actuation electrode as can be appreciated by one of skill in theart. Variable capacitor 400 can also include a stationary capacitiveelectrode SCE positioned on the top surface of substrate 402 and beneathmovable capacitive electrode MCE2. Movable actuation electrodes MAE1,MAE2, MAE3, and MAE4 can be connected to a voltage supply VS viaconductive line CL1. Stationary actuation electrodes SAE1 and SAE2 canbe connected to voltage supply VS via conductive line CL2. Voltagesupply VS can apply one voltage potential at movable actuationelectrodes MAE1 and MAE2 and a different voltage potential at stationaryactuation electrodes SAE1 and SAE2. The equal and opposite electricalcharge causes an electrostatic force to pull movable actuationelectrodes MAE1, MAE2, MAE3, and MAE4, and movable component MC, towardsstationary actuation electrodes SAE1 and SAE2 in a direction indicatedby direction arrow 502. Tethers T1, T2, T3, T4, T5, and T6 can produce abiasing force to oppose movement of movable component MC in directionindicated by arrow 502. Movable component MC can move towards substrate402 only when the voltage applied across the stationary actuationelectrodes (SAE1 and SAE2) and the movable actuation electrodes (MAE1,MAE2, MAE3, and MAE4) is great enough to overcome the resistive force oftethers T1, T2, T3, T4, T5, and T6. Movable component MC is shown inposition when the voltage applied by voltage supply VS is 0 Volts. Inthis embodiment, when voltage supply VS is 0 Volts, movable capacitiveelectrode MCE2 is separated from stationary capacitive electrode byabout 0.5 micrometers. Additionally, in this embodiment, when voltagesupply VS is 0 Volts, movable actuation electrodes MAE3 and MAE4 can beseparated from SAE2 and SAE1, respectively, by about between 1.5 and 2.0micrometers.

[0099] Variable capacitor 400 can also include a stationary capacitiveelectrode SCE attached to the top surface of substrate 402 and beneathmovable capacitive electrode MCE1 and MCE2. Electrodes SCE, MCE1, andMCE2 can be electrically connected to a signal line SL for supplying asignal, typically AC, to variable capacitor 400 from other electricalcircuitry (not shown). Movable capacitive electrodes MCE1 and MCE2 canbe moved to different positions with respect to stationary capacitiveelectrode SCE when voltage is applied to movable actuation electrodes(MAE1, MAE2, MAE3, and MAE4) and stationary actuation electrodes (SAE1and SAE2) for moving movable component MC such that capacitance ischanged between movable capacitive electrodes MCE1 and MCE2 andstationary capacitive electrode SCE.

[0100] Referring to FIG. 6, another cross-sectional side view ofvariable capacitor 400 is illustrated. The voltage applied acrossmovable actuation electrodes (MAE1, MAE2, MAE3, and MAE4) and stationaryactuation electrodes (SAE1 and SAE2) is greater than a 0 Volts forovercoming the resistive force of tethers T1, T2, T3, T4, T5, and T6.With the applied voltage set greater than 0 Volts, peripheral portion406 can be positioned closer to substrate 402 than when the appliedvoltage is set to 0 (as shown in FIG. 2). Interior portion 408 can alsomove closer to substrate 402 when peripheral portion 406 is movedtowards substrate 402 due to the attachment of interior portion 408 toperipheral portion 406 with connectors 410 and 412.

[0101] Interior portion 408 can be substantially, mechanically isolatedfrom peripheral portion 406 because interior portion 408 is onlyattached to peripheral portion 406 via connectors 410 and 412.Therefore, the deformation of interior portion 408 is substantiallylimited when its peripheral portion 406 moves towards substrate 402. Ifonly two connectors are used as in this exemplary embodiment, connectors410 and 412 can include a cross-sectional area large enough to suppresstorsional motion. According to one embodiment connectors 410 and 412 aresubstantially wider than the thickness of movable component MC andsubstantially shorter than they are wide. Connectors 410 and 412 canrange in width between 0.5 micrometers and 100 micrometers. Thethickness of movable component MC can be between about 0.5 and 20microns. The width of connectors 410 and 412 can be greater than 5 timesthe thickness. The length of connectors 410 and 412 can be about 5micrometers. This is advantageous because interior portion 408 and itsattached movable capacitive electrode MCE can remain substantiallyplanar when moved towards substrate 402.

[0102] Referring to FIG. 7, a top view of variable capacitor 400 isillustrated. Movable capacitive electrode MCE1 can be connected tosignal line SL via conduits C1 and C2 disposed on top of movablecomponent MC. Conduits C1 and C2 can extend from movable capacitiveelectrode MCE along tethers T6 and T3, respectively, for connection tosignal line SL.

[0103] Referring to FIG. 7, movable capacitive electrode MCE1 can have ahexagonal shape with a diameter d1 of between about 25 micrometers and 2millimeters. In one embodiment, peripheral component 406 has a width ofabout 45 micrometers. Alternatively, peripheral component 406 can rangebetween 25 micrometers and 1 millimeter. Tethers T1, T2, T3, T4, T5, andT6 can have a length between about 100 and 250 micrometers.

[0104]FIG. 8 illustrates a top perspective view of variable capacitor400 with the voltage applied to electrodes MAE1, MAE2, MAE3, and MAE4and SAE is set to a voltage greater than 0 Volts for overcoming theresistive force of tethers T1, T2, T3, T4, T5, and T6. With the appliedvoltage set to a voltage greater than 0 Volts, movable component MC canbe positioned closer to substrate 200 than when the applied voltage isset to 0 (as shown in FIG. 2).

[0105] Simulations have demonstrated that the embodiment shown in FIGS.4-7 can achieve a high impedance control input (with minimum leakage upto about 100 Volts), an operating frequency of between 0 and 10 GHz, aseries resistance of less than 0.5 ohms and typically less than 0.2ohms, a vibration sensitivity of less than 0.5% capacitance variationfor 0.3 g @ 1 kHz, and a control input cut-off frequency of greater and20 kHz.

[0106] One important consideration concerns the harmonic behavior of thevariable capacitor. The variable capacitor is typically operated innormal air conditions with a very small air gap (between about 0.5 and0.01 micrometers). When the movable component acts as a piston, the airin the air gap between the movable component and the substrate can actas a squeeze-film and its effects can be strongly dependent on thefrequency of the motion. Apertures can be formed in a movable componentto reduce the effects of the air in the air gap between the movablecomponent and the substrate.

[0107] The quality of resonance (Q) can also be measured for theembodiment shown in FIGS. 4-7. Generally, Q refers to powerdissipation/(energy stored*radian frequency). There are two resonancequalities of interest with regard to this embodiment. One resonancequality of interest is the mechanical quality of resonance of movablecomponent MC. This can typically be low due to air damping. However, ifit is too low, it will slow down the response of variable capacitor 400.A mechanical quality Q on the order of unity is desirable. This can bedesigned through the gap selected between movable component MC andsubstrate 402 and spacing in movable component MC and size/quantities ofapertures (described below).

[0108] Another resonance quality Q is the electrical resonance qualityof variable capacitor 400. To first order, this resonance quality Q isprovided by the following equation:$\frac{1}{\left( {{radian}\quad {frequency}*{capacitance}*{series}\quad {resistance}} \right)}$

[0109] This quality of resonance Q should be as high as possible, suchas greater than 100. This can be achieved with a low resistance conduit.

[0110] Another key parameter is the tuning ratio which is the ratiobetween the maximum and minimum capacitances achievable by the variablecapacitor. This should be as high as possible with a value greater than4 being useful and a value greater than 8 considered very desirable.This is achieved by enabling the gap between movable capacitiveelectrode MCE and station capacitive electrode SCE to be varied stablyover a wide range and by low parasitics such as fixed capacitances atthe edges and at the conduits.

[0111] A mechanical resonance frequency calculation can be performed fora small-signal excitation at an “undeformed” state of variable capacitorwith voltage set to 0. Damping effects can be considered. Additionally,experiments demonstrate that the variable capacitor embodiment shown inFIG. 4-7 can have a resonance frequency above 20 kHz. The firstresonance mode occurs at 21.6 kHz. The displacement of movable componentMC with respect to substrate 402 (z-displacement) for this mode is a“flapping” mode.

[0112]FIG. 9 illustrates a computer simulation model of thez-displacement of movable component MC at the first resonance mode of21.6 kHz. The edges of movable component MC exhibit the largestdisplacement. The edges are in phase, meaning that the two edges aremoving in the same direction. A second resonance mode occurs at 23.4kHz. The second resonance mode is a “torsional” mode, where the edgesmove out-of-phase (one edge goes up while the other edge goes down).

[0113]FIG. 10 illustrates a graph showing displacement of center C (μm)of movable component MC versus voltage applied to electrodes MAE andSAE. FIG. 11 illustrates a computer simulation model of thez-displacement of movable component MC for an actuation voltage of about25 Volts. Although a gap ratio of 3 is nominally stable for parallelplate actuation, the deformation of the plates during actuation createsnon-planarity and thus introduces instability. This is solved byincreasing the gap ratio to grater than 3 to provide margin. However,increasing the gap ratio also increases the control voltage for a givencapacitor gap so it should not be increased more than necessary. Typicalembodiments have gap ratios of about 4. Deformation is not due to theelectrostatic force acting on interior portion 408 (shown in FIG. 4),but due to the tilt of peripheral portion 406 (shown in FIG. 4) atpoints where interior portion 408 is attached to peripheral portion 406(i.e., where connectors 410 and 412 shown in FIG. 4 contact interiorportion 408). Bending of moving capacitive electrodes MCE1 and MCE2 canhave an adverse effect on the capacitance value.

[0114] Referring to again FIG. 5, any radio frequency (RF) signals onsignal line SL can generate an electrical force on movable component MCdue to the electrical charge generated on stationary capacitiveelectrode SCE and movable capacitive electrodes MCE1 and MCE2. Becausethe electrical force is related to the square of the voltage and thearea of actuation, the AC voltage can introduce a net DC force betweenstationary capacitive electrode SCE and movable capacitive electrodesMCE1 and MCE2. For example, when an RF-signal of 0.5 V_(pp) is applied,the equivalent of a 0.18 DC Volts is applied between stationarycapacitive electrode SCE and movable capacitive electrodes MCE1 andMCE2. For example, when 15 Volts is applied over an air-gap of 1.5micrometers, an equivalent pressure of about 885 Pa is generated. Incontrast, for example, when 0.18 Volts is applied over an air-gap of 0.5micrometers, an equivalent pressure of about 1.15 Pa is generated. Evenfor a displacement as high as 0.4 micrometers, the equivalent pressureof actuation electrodes MAE1, MAE2, MAE3, MAE4, SAE1, and SAE2 is about1645 Pa. In contrast, the equivalent pressure from 0.18 Volts appliedover the remaining 0.1 micrometers is 29 Pa. Therefore, movablecomponent MC position is primarily determined by actuation voltage untilthe RF gap is very small as long as the areas of the actuationelectrodes are on the order of or significantly larger than the area ofthe capacitance electrodes.

[0115]FIG. 12 illustrates a graph showing capacitance (pF) betweenstationary capacitive electrode SCE and movable capacitive electrodesMCE1 and MCE2 versus voltage applied to electrodes SAE1, SAE2, MAE1,MAE2, MAE3, and MAE4 shown in FIG. 5. The minimum capacitance in thisembodiment with actuation voltage set at 0 Volts is about 2.1 pF. Thecapacitance ratio is about 1:3.6.

[0116] The robustness of variable capacitor 400 (shown in FIG. 4)against residual stress deformations can be a good indicator of therobustness of variable capacitor 400 against temperature changes.Allowing movable component MC to rotate to a certain degree generatesmost of the residual stress effects only in the XY plane. FIGS. 13A and13B illustrate different computer simulation models of the deformationof movable component MC. FIG. 13A illustrates a computer simulationmodel of the deformation of movable component MC for a residual stressvalue of 120 MPa (uniform stress across movable component MC). Thedisplacement in the x and y directions in this example are smaller than0.5 micrometers while displacement in the z direction is as small as0.001 micrometers. Thus, the capacitance in this example is notadversely affected by either the residual stress or the difference inthermal expansion between the movable component MC and substrate 402(shown in FIG. 4).

[0117] The robustness of movable component MC (shown in FIG. 4) againststress gradients is also important. As referred to herein, the stressgradient means the varying of the residual and thermal stress levelsacross the thickness of movable component MC. Stress gradients cantypically range between 1 and 10 MPa. FIG. 13B illustrates a computersimulation model of deformation of movable component MC under a stressgradient between +10 and −10 MPa. The warping of interior portion 408can have a great impact on the capacitance and capacitance ratio ofvariable capacitor 400 (shown in FIG. 4).

[0118]FIG. 14 illustrates a computer simulation model, generallydesignated 1400, of an equivalent circuit of variable capacitor 400shown in FIG. 4. In this example, the SABER™ simulator (available fromAnalogy, Inc. of Beaverton, Oreg.) can be used for modeling variablecapacitor 400. Simulation model 1400 can include six beams for thetethers 1402, 1404, 1406, 1408, 1410, and 1412 and associated beams withelectrodes 1414, 1416, 1418, 1420, 1422, and 1424, respectively.Simulation model 1400 can also include a connector models 1426 and 1428,and a capacitive electrode model CEM.

[0119]FIGS. 15A, 15B, and 15C illustrate computer simulation models ofthe deformation of different interior portions (such as interior portion408 shown in FIG. 4) under a stress gradient between + and − MPa. FIG.15A illustrates a square-shaped interior portion 1500 under the stressgradient. FIG. 15B illustrates a hexagonal-shaped interior portion 1502under the stress gradient. FIG. 15C illustrates a circular-shapedinterior portion 1504 under the stress gradient. Table 1 below indicatesthe maximum and minimum z-displacements for each of the three interiorportion shapes. TABLE 1 Maximum and minimum z-displacements for threeinterior portion shapes Maximum Z Minimum Z Delta Z square 1.893 μm−0.804 μm 2.697 μm hexagon 1.420 μm −0.933 μm 2.353 μm circle 1.256 μm−0.930 μm 2.186 μm

[0120] Based on the simulation results, square-shaped interior portion1500 provides the largest maximum displacement, which is located at thecorners. The center of square-shaped interior portion 1500 provides thesmallest displacement of the three interior portion shapes. This resultis explained by the fact that the axis of square-shaped interior portion1500, with the same total area, is shorter than for the other twoshapes. The average displacement is an indication of the sensitivity ofthe capacitance to stress gradients. For the maximum displacement, themost robust shape against stress gradient is the circular plate with thehexagonal design of FIG. 4 being nearly as good.

[0121] An interesting observation is that the iso-displacement curvesare elliptical. FIG. 16 illustrates a computer simulation model of anexemplary elliptically-shaped interior portion 1600 with the same areaunder the same stress gradients. In this example, the edges of theellipse do not move upwards or downwards: the bending of the axis andthe bending perpendicular to the axis compensate each other along theelliptical contour. The center of elliptically-shaped interior portion1700 is almost 1.4 μm below the zero displacement point. The capacitancechange is higher in elliptically-shaped interior portion 1700 than incircular-shaped interior portion 1504 (shown in FIG. 15C).

[0122] A low sensitivity to acceleration is an important requirement forvaractor capacitor. In particular, the change of the capacitance due tovibration or acceleration is expected to be an important source of noisefor the variable capacitor. For computer simulations, a constantacceleration was applied to an undeformed interior portion (such asinterior portion 408 shown in FIG. 4). Several values can be considered,showing a linear behavior of the displacement even for relatively highvalues of acceleration. FIG. 17 illustrates a computer simulation modelof the deformation of an interior portion 1700 for an acceleration of100 g. The center displacement of interior portion 1700 is about 0.12μm. Therefore, the acceleration sensitivity is about 1.2 [nm/g]. For aconstant acceleration of 0.3 g, such as the value expected for thevibration, the maximum displacement is only 3.6 Å. The capacitancechange under these conditions is lower than 0.5%. From the mechanicalperspective, the cut-off frequency for the mechanical Low-Pass-Filtercan be targeted to be higher than 20 kHz. Therefore, the response ofinterior portion 1700 to the acceleration will be fairly independent ofthe frequency, up to 20 kHz. In other words, a vibration of 0.3 g at 1kHz will provide a capacitance change up to 0.5% of the capacitance.

[0123] Table 2 below indicates a summary of specifications for oneembodiment of a variable capacitor such as variable capacitor 400 shownin FIG. 4. TABLE 2 Summary of Specifications Parameter Value V_(control)27 V Resonance 21.6 kHz frequency C_(min) 2.2 pF (dc) Capacitance ratiomaximum 1:3.6 Vibration sensitivity <0.5%/0.3 g

[0124] The actuation voltage and resonance frequency of a variablecapacitor such as variable capacitor 400 (shown in FIG. 4) can bedependent upon the width of a peripheral portion (such as peripheralportion 406 shown in FIG. 4) and the length of the tethers (such astethers T1, T2, T3, T4, T5, and T6 shown in FIG. 4). FIG. 18 illustratesa graph showing different tether lengths and peripheral portion widthsversus actuation voltage for a variable capacitor (such as variablecapacitor 400 shown in FIG. 4). FIG. 19 illustrates a graph showingdifferent tether lengths and peripheral portion widths versus resonancefrequency for a variable capacitor (such as variable capacitor 400 shownin FIG. 4). As shown, a variable capacitor having a tether length of 75micrometers and peripheral portion width of 75 micrometers can achieve aresonance frequency of 35.9 kHz.

[0125]FIG. 20 illustrates a computer simulation model of thez-displacement of the first resonance mode of a variable capacitor 2000having a tether length of 75 micrometers and peripheral portion width of75 micrometers. The resonance frequency of the first resonance mode isabout 33.9 kHz. The resonance frequency of the second resonance mode isabout 59.9 kHz. As shown in FIG. 20, interior portion 2002 remainsrelatively rigid and most of the deformation occurs at tethers T1, T2,T3, T4, T5, and T6, along with a tilt in peripheral portion 2004.

[0126]FIG. 21 illustrates a computer simulation model of thez-displacement of a variable capacitor 2000 having a tether length of 75micrometers and peripheral portion width of 75 micrometers at anactuation voltage set at 14 Volts.

[0127]FIG. 22 illustrates a graph showing displacement of the center ofa variable capacitor 2000 having a tether length of 75 micrometers andperipheral portion width of 75 micrometers versus voltage applied to theactuation electrodes.

[0128]FIG. 23 illustrates a computer simulation model of thez-displacement of an interior portion 2300 of a variable capacitor 2302exposed to a temperature difference of 1000 Celsius. In this example,the z-displacement of interior portion 2300 is about 0.002 micrometers.Therefore, temperature has little effect on the capacitance values inthis embodiment.

[0129]FIG. 24 illustrates a computer simulation model of deformation ofan interior component 2400 having a tether length of 75 micrometers andperipheral portion width of 75 micrometers under a stress gradientbetween +10 and −10 MPa.

[0130]FIG. 25 illustrates a computer simulation model of the deformationof an interior component 2500 having a tether length of 75 micrometersand peripheral portion width of 75 micrometers for an acceleration of100 g. The z-displacement is less than about 0.03 micrometers for 100 gacceleration (i.e., 0.1 nm for an 0.3 g acceleration). Therefore, thecapacitance can be modified by a factor of about 0.04% with an air gapof 0.26 micrometers.

[0131] Referring to FIG. 26, a top perspective view of another exemplaryvariable capacitor, generally designated 2600, is illustrated. Variablecapacitor 2600 can include an interior portion 2602 having a pluralityof apertures 2604 extending from a top surface 2606 to an opposingbottom surface (not shown). Apertures 2604 can also extend through amovable capacitive electrode MCE1 attached to top surface 2606 and amovable capacitive electrode (not shown), if any, attached to theopposing bottom surface (not shown). Apertures 2604 can function toventilate variable capacitor 2600. In this embodiment, interior portion2602 includes thirty-seven apertures that are evenly distributed onsurface 2606. Alternatively, interior portion 2602 can include 7, 27,169, 721, or any suitable number of apertures.

[0132] Referring to FIG. 27A, a cross-sectional side view of oneaperture, generally designated 2700, of interior portion 2602 isillustrated. In this embodiment, interior portion 2602 includes movablecapacitive electrodes MCE1 and MCE2 attached to top surface 2604 and abottom surface 2702, respectively. In this embodiment, aperture 2700 iscylindrically-shaped with a diameter of about 5 micrometers.Additionally, in this embodiment, distance d between the edges ofinterior portion 2602 and movable capacitive electrode (MCE1 or MCE2) isbetween about 0 and 8 micrometers.

[0133] Referring to FIG. 27B, a cross-sectional side view of anotheraperture, generally designated 2704, of interior portion 2706 isillustrated. In this embodiment, a movable capacitive electrode 2708 canextend inside aperture 2704. Movable capacitive electrode 2708 canconform to and contact movable capacitive electrode 2710. Thisembodiment can be advantageous because the area of the capacitiveelectrode is not reduced as much for a given aperture size.

[0134]FIG. 28 illustrates a graph showing the cut-off frequency of avariable capacitor versus the number of apertures in an interior portionof the variable capacitor. Extrapolating from the graph, the cut-offfrequency is about 20 kHz for 721 apertures.

[0135] The number of holes can be selected in order to half the distancebetween the outer row of holes and the edges of the hexagonally-shapedinterior portion at every increment. This leads to a series of thenumber of holes as follows: 0, 1, 7, 37, 169, 721, etc. At 169 holes,the pitch is 27 micrometers in one embodiment.

[0136] Referring to FIG. 29, a graph showing the damping and tetherforces versus frequency for different number of apertures isillustrated. In the low-frequency regime, the air acts as a damper. Inthe high-frequency regime, the air acts as a spring.

[0137]FIG. 30 illustrates a graph showing the damping coefficient as afunction of the frequency for different numbers of apertures. The forceat high frequency is relatively independent of the number of aperturesbecause the volume of air being squeezed remains relatively constant.

[0138]FIG. 31 illustrates a graph showing harmonic analysis of avariable capacitor having an interior portion with 37 apertures. In thelow-frequency regime, the variable capacitor is overdamped exhibitingthus a low-pass filter characteristic. At 62 kHz all curves showresonance peaks. The resonance frequencies are determined by the mass ofthe structures and the combined stiffness of squeezed film and of thesolid structure itself. At this pressure (1 bar) and this air gap (0.25micron) the stiffness of the air is approx. twice the stiffness of thestructure itself.

[0139]FIG. 32 illustrates a graph showing the cut-off frequency fordifferent aperture numbers. Table 3 below indicates the cut-offfrequency for different aperture numbers. TABLE 3 Apertures numbers andCut-off Frequency Cut-off Number of frequency Apertures [Hz] 1 33 7 5137 312 169 2420

[0140] From extrapolation, 17 kHz can be expected as a cut-off frequencyfor 721 apertures. In one embodiment, a distance of 6 micrometers isprovided between a capacitive electrode and edge of the interior portionat the aperture. In the configuration of this embodiment, each 5micrometer diameter hole in the interior portion can have a capacitiveelectrode opening of 17 micrometers in diameter. Thus, resulting in aneffective loss for the capacitance area.

[0141]FIG. 33 illustrates a graph showing the effective area of thecapacitive electrode as a function of the number of apertures for fourdifferent cases according to the minimum distance between the gold layerand the opening of the interior portion (8 μm, 6 μm, 2 μm and 0 μm).Regarding 8 μm, the capacitance is reduced by 70% for 25 apertures.Regarding 2 μm, the capacitance is reduced by 40% for 169 apertures. Inthe embodiment shown in FIG. 27B where the aperture is defined by themetal rather than the hole in the structural layer of movable componentMC, the capacitance can be reduced by less than 15%.

[0142] In order to achieve larger capacitance values, the variablecapacitor can be made large or two or more variable capacitors can beconnected in parallel. The maximum size of the capacitor is constrainedby mechanical considerations (including release time, mechanicalresonance frequency, damping and stress deformation), and thus theparallel connection of smaller capacitors can be advantageous. Referringto FIGS. 34 and 35, different top views of exemplary cascadearrangements of a plurality of variable capacitors are illustrated.Referring specifically to FIG. 34, variable capacitors 3400 are arrangedin a rectangular shape. Referring to FIG. 35, variable capacitors 3500are arranged in a fanned-shape. A signal line (not shown) having a totallength of about 600 micrometers and a width of about 5 micrometers(impedance matched to 50 ohms). The inductance inserted by this longsignal line can result in a self-resonance frequency in the order of 10GHz, showing a degradation of the quality factor even at frequenciessuch as 4 GHz. These interconnects should be kept short as possible.Thus, a center feed to the array is desirable to minimize parasitics andmaximize self-resonance frequency.

[0143] The variable capacitor arrangements shown in FIGS. 34 and 35 canhave the specifications shown in Table 4 below. TABLE 4 Summary ofSpecifications Parameter Simulated V_(control) 14.6 V Resonance 33.9 kHzfrequency C_(min) 2.6 pF (neglecting area loss due to apertures)Capacitance ratio maximum 1:4 Q Greater than 35 @ 4.5 GHz Cut-offfrequency 2.4 kHz (with of the LPF 169 apertures)

[0144]FIGS. 36A and 36B illustrate a computer simulation model,generally designated 3600, and RF results of computer simulation model3600, for an equivalent circuit of four variable capacitors (such asvariable capacitor 400 shown in FIG. 4) arranged in parallel. Referringto FIG. 36A, the HFSS electromagnetic, full-wave simulator (availablefrom Ansoft Corporation of Pittsburgh, Pa.) can be used for modelingfour variable capacitors 3602, 3604, 3606, and 3608. Model 3600 caninclude a connection block 3610 representing the connection of variablecapacitors 3602, 3604, 3606, and 3608. Additionally, model 3600 caninclude a block 3612 representing a line out of the measurement pads.

[0145] Referring to FIG. 36B, line 3614 shows that the capacitance doesvary some with frequency due to the interconnecting scheme. Line 3616shows the electrical resonance quality Q falling with frequency. In thisexample, resonance quality Q includes the degrading effects of theinterconnects. A Smith chart, generally designated 3618, shows that thecircuit behaves as a capacitor over the whole frequency range.

[0146]FIGS. 37A and 37B illustrate top perspective views of otherexemplary variable capacitors. Referring specifically to FIG. 37A, a topperspective view of another exemplary variable capacitor, generallydesignated 3700, utilizing a rectangular geometry including a suspended,movable component MC. Movable component MC can include movable actuationelectrodes MAE1 and MAE2 and a movable capacitive electrode MCE. In thisembodiment, electrodes MAE1, MAE2, and MCE are attached to a top surfaceof movable component MC. Alternatively, electrodes MAE1, MAE2, and MCEcan be attached on the underside of movable component MC or on both thetop and bottom surfaces. Actuation electrode MAE1 and MAE2 andcapacitive electrode MCE can be electrically isolated via movablecomponent MC.

[0147] Variable component 3700 can also include tethers T1, T2, and T3attached to movable component MC and posts (not shown) for suspendingmovable component MC above a substrate 3702. Stationary actuationelectrodes SAE1 and SAE2 can be disposed on the top surface of substrate3702 and directly beneath movable actuation electrodes MAE1 and MAE2,respectively. A stationary capacitive electrode SCE can be disposed onthe top surface of substrate 3702 and directly beneath movablecapacitive electrode MCE. A voltage supply VS can be connected at oneterminal to movable actuation electrodes MAE1 and MAE2 and at anotherterminal to stationary actuation electrodes SAE1 and SAE2. Voltagesupply VS can apply a potential difference between the movable actuationelectrodes (MAE1 and MAE2) and the stationary electrodes (SAE1 and SAE2)such that, at after a voltage threshold V_(T) is achieved, movablecomponent MC deflects towards substrate 3602. Electrodes SCE and MCE canbe electrically connected to a signal line SL for supplying a signal,typically AC, to variable capacitor 3600 from other electrical circuitry(not shown).

[0148]FIG. 37B illustrates a top perspective view of another exemplaryvariable capacitor, generally designated 3704, including a suspended,movable component MC. Movable component MC can include movable actuationelectrodes MAE1 and MAE2 and a movable capacitive electrode MCE. In thisembodiment, electrodes MAE1, MAE2, and MCE are attached to a top surfaceof movable component MC. Alternatively, electrodes MAE1, MAE2, and MCEcan be attached on the underside of movable component MC or on both thetop and bottom surfaces. Actuation electrode MAE and capacitiveelectrode MCE can be electrically isolated via movable component MC.

[0149] Variable component 3704 can also include tethers T1, T2, T3, T4,and T5 attached to movable component MC and posts (not shown) forsuspending movable component MC above a substrate 3706. Stationaryactuation electrodes SAE1 and SAE2 can be disposed on the top surface ofsubstrate 3706 and directly beneath movable actuation electrodes MAE1and MAE2, respectively. A stationary capacitive electrode (not shown)can be disposed on the top surface of substrate 3706 and directlybeneath movable capacitive electrode MCE. A voltage supply VS can beconnected at one terminal to movable actuation electrodes MAE1 and MAE2and at another terminal to stationary actuation electrodes SAE1 andSAE2. Voltage supply VS can apply a potential difference between themovable actuation electrodes (MAE1 and MAE2) and the stationaryelectrodes (SAE1 and SAE2) such that, at after a voltage threshold V_(T)is achieved, movable component MC deflects towards substrate 3706. Thestationary capacitive electrode and movable capacitive electrode MCE canbe electrically connected to a signal line SL for supplying a signal,typically AC, to variable capacitor 3704 from other electrical circuitry(not shown).

[0150] According to one embodiment, isolation bumps can be included witha variable capacitor (such as variable capacitor 400 shown in FIG. 4)for preventing movable capacitive electrode (such as movable capacitiveelectrode MCE2 shown in FIG. 5) and/or movable actuation electrode (suchas movable actuation electrodes MAE3 and MAE4 shown in FIG. 5) fromcontacting a stationary capacitive electrode (such as stationarycapacitive electrode SCE shown in FIG. 5) and/or stationary actuationelectrodes (such as stationary actuation electrodes SAE1 and SAE2 shownin FIG. 5). The use of isolation bumps can enable variable capacitorswith high capacitance ratio and electromechanical stability.

[0151]FIGS. 38 and 39 illustrate different cross-sectional side views ofa variable capacitor having isolation bumps. Referring to FIG. 38, across-sectional side view of a variable capacitor, generally designated3800, having isolation bumps IP1, IP2, and IP3 is illustrated. Variablecapacitor 3800 can include a movable component MC having movableactuation electrodes 3802 and 3804 positioned on a top and bottomsurface 3806 and 3808, respectively. Movable component MC can includemovable capacitive electrodes 3810 and 3812 positioned on a top andbottom surface 3806 and 3808, respectively. Variable capacitor 3800 canalso include a substrate 3814 including a top surface 3816 having astationary capacitive electrode 3818 deposited thereon.

[0152] Substrate 3814 can include one or more substrate layers,generally designated SL, including a stationary actuation electrode 3820positioned therein. Substrate layers SL can also include a capacitorinterconnect CI for connecting stationary capacitive electrode 3818 to asignal line (not shown). In this embodiment, substrate layers SL includea base substrate layer BSL, a first metal layer M1, a first substratelayer S1, a second metal layer M2, and a second substrate layer S2.

[0153] In this embodiment, one or more sacrificial layers (not shown)can be used during a fabrication process for constructing movablecomponent MC (FIG. 38). The sacrificial layers can subsequently beremoved by a suitable process to form the gap, generally designated G,between movable component MC and substrate 3814. In this embodiment, gapG can extend different distances between movable component MC andsubstrate 3814. For example, a gap distance D1 between movable actuationelectrode 3804 and surface 3816 of substrate 3814 can be about 2.5micrometers with a range between about 0.5 and 10 micrometers. In thisembodiment, gap distance D1 is the total of the following thicknesses:thickness of stationary capacitor 3818, the thickness of a firstsacrificial layer for forming gap G, and the thickness of a secondsacrificial layer for forming gap G. Additionally, for example, a gapdistance D2 between isolation bump IP1 and surface 3816 of substrate3814 can be about 2.0 micrometers in the embodiment and can be somewhatsmaller than the overall actuation gap limited only be the fabricationprecision. In this embodiment, gap distance D2 is the thickness of thefirst sacrificial layer. Additionally, for example, a gap distance D3between movable capacitive electrode 3812 and surface 3816 of substrate3814 can be between about 0.5 and 20 micrometers. In this embodiment,gap distance D3 is the thickness of the first and second sacrificiallayers. Additionally, for example, a gap distance D4 between isolationbump IP2 and stationary capacitive electrode 3818 can be 2.0 micrometersand range from between about 0.5 and 20 micrometers. In this embodiment,gap distance D4 is the thickness of the first sacrificial layer.Additionally, for example, a gap distance D5 between isolation bump IP3and stationary capacitive electrode 3818 can be 2.0 micrometers andrange from between about 0.5 and 20 micrometers. In this embodiment, gapdistance D5 is the thickness of the first sacrificial layer.

[0154] Referring to FIG. 39, actuation voltage has been applied toactuation electrodes 3802, 3804, and 3820 for moving movable componentMC to a closed position such that isolation bumps IP1, IP2, and IP3contact substrate 3814. Isolation bumps IP1, IP2, and IP3 can preventmovable capacitive electrode 3812 from contacting stationary capacitiveelectrode 3818. In this embodiment, capacitive electrodes 3812 and 3818can be separated by a distance of about 0.5 micrometers when movablecomponent MC is in the closed position.

[0155] The equivalent actuation gap of the embodiment shown in FIGS. 38and 39 is provided by the following equation (wherein S1 represents thethickness of first substrate layer S1, S2 represents the thickness ofsecond substrate layer S2, M2 represent the thickness of second metallayer M2, SAC1 represents the thickness of the first sacrificial layer,SAC2 represents the thickness of the second sacrificial layer, M3represents the thickness of stationary capacitive electrode 3818 and ksrepresents the relative dielectric constant of the substrate):${{Equivalent}\quad {electrical}\quad {gap}} = {\frac{{S1} + {S2} + {M2}}{ks} + {SAC1} + {SAC2} + {M3}}$

[0156] In this embodiment, the equivalent electrical gap is about 5micrometers. In this embodiment, the mechanical displacement is limitedto the thickness of the first sacrificial layer. The actuation voltagescales as V α airgap{circumflex over ( )}(3/2). For an air gap of 1.5micrometers, the actuation voltage is 15 Volts. With an equivalent airgap of 5 micrometers, the actuation voltage is 91 Volts. With thevariable capacitor 400 (FIG. 4) including isolation bumps such asisolation bumps IP1, IP2, and IP3 shown in FIGS. 38 and 39, a minimumcapacitance of 0.5 picoFarads can be achieved. Additionally, in such aconfiguration, the capacitance ratio is about 4.

[0157] Referring to FIG. 40, a cross-sectional side view of anothervariable capacitor, generally designated 4000, having an isolation bumpIP is illustrated. Variable capacitor 4000 can include a movablecomponent MC having movable actuation electrodes 4002 and 4004positioned on a top and bottom surface 4006 and 4008, respectively.Movable component MC can include movable capacitive electrodes 4010 and4012 positioned on a top and bottom surface 4006 and 4008, respectively.Variable capacitor 4000 can also include a substrate 4014 including atop surface 4016 having a stationary capacitive electrode 4018 depositedthereon.

[0158] Substrate 4014 can include one or more substrate layers,generally designated SL, including a stationary actuation electrode 4020positioned therein. Substrate layers SL can also include a capacitorinterconnect CI for connecting stationary capacitive electrode 4018 to asignal line (not shown). In this embodiment, substrate layers SL includea base substrate layer BSL, a first metal layer M1, a first substratelayer S1, a second metal layer M2, and a second substrate layer S2.

[0159] In this embodiment, one or more sacrificial layers (not shown)can be used during a fabrication process for constructing movablecomponent MC (FIG. 40). The sacrificial layers can subsequently beremoved by a suitable process to form the gap, generally designated G,between movable component MC and substrate 4014. In this embodiment, gapG can extend different distances between movable component MC andsubstrate 4014. For example, a gap distance D1 between movable actuationelectrode 4004 and surface 4016 of substrate 4014 can be about 2.5micrometers with a range between about 0.5 and 10 micrometers. In thisembodiment, gap distance D1 is the total of the following thickness:thickness of stationary capacitor 4018, the thickness of a firstsacrificial layer for forming gap G, and the thickness of a secondsacrificial layer for forming gap G. Additionally, for example, a gapdistance D2 between isolation bump IP and surface 4016 of substrate 4014can be between about 0.5 and 20 micrometers. In this embodiment, gapdistance D2 is the thickness of the first sacrificial layer.Additionally, for example, a gap distance D3 between movable capacitiveelectrode 4012 and surface 4016 of substrate 4014 can be about 2.0 andrange from between about 0.5 and 20 micrometers. In this embodiment, gapdistance D3 is the thickness of the first and second sacrificial layers.The gap ratio is about 0.55 in this embodiment.

[0160] The equivalent actuation gap of the embodiment shown in FIG. 40is provided by the following equation (wherein S2 represents thethickness of second substrate layer S2, SAC1 represents the thickness ofthe first sacrificial layer, SAC2 represents the thickness of the secondsacrificial layer, M3 represents the thickness of stationary capacitiveelectrode 4018 and ks represents the relative dielectric constant of thesubstrate):${{Equivalent}\quad {electrical}\quad {gap}} = {\frac{S2}{ks} + {SAC1} + {SAC2} + {M3}}$

[0161] In this embodiment, the equivalent electrical gap is about 3.3micrometers. In this embodiment, the mechanical displacement is limitedby the thickness of the first sacrificial layer. For an air gap of 1.5micrometers, the actuation voltage is 15 Volts. With an equivalent airgap of 5 micrometers, the actuation voltage is 49 Volts. With thevariable capacitor 400 (FIG. 4) including isolation bumps such asisolation bump IP shown in FIG. 40, a minimum capacitance of 0.5picoFarads can be achieved. Additionally, in such a configuration, thecapacitance ratio is about 4.

[0162] Referring to FIG. 41, a cross-sectional side view of anothervariable capacitor, generally designated 4100, having an isolation bumpIP is illustrated. Variable capacitor 4100 can include a movablecomponent MC having movable actuation electrodes 4102 and 4104positioned on a top and bottom surface 4106 and 4108, respectively.Movable component MC can include movable capacitive electrodes 4110 and4112 positioned on a top and bottom surface 4106 and 4108, respectively.Variable capacitor 4100 can also include a substrate 4114 including atop surface 4116 having a stationary capacitive electrode 4118 depositedthereon.

[0163] Substrate 4114 can include one or more substrate layers,generally designated SL, including a stationary actuation electrode 4120positioned therein. Substrate layers SL can also include a capacitorinterconnect CI for connecting stationary capacitive electrode 4118 to asignal line (not shown). In this embodiment, substrate layers SL includea base substrate layer BSL, a first metal layer M1, a first substratelayer S1, a second metal layer M2, and a second substrate layer S2.

[0164] Movable component MC can also include a planarization dielectricthat is compatible with the process attached to bottom surface 4108. Aexemplary dielectric choice is to use silicon dioxide for theplanarization dielectric. This planarization oxide PO can benon-conductive for preventing movable capacitive electrode 4112 fromelectrically communicating with stationary capacitive electrode 4118.

[0165] In this embodiment, one or more sacrificial layers (not shown)can be used during a fabrication process for constructing movablecomponent MC (FIG. 41). The sacrificial layers can subsequently beremoved by a suitable process to form the gap, generally designated G,between movable component MC and substrate 4114. In this embodiment, gapG can extend different distances between movable component MC andsubstrate 4114. For example, a gap distance D1 between movable actuationelectrode 4104 and surface 4116 of substrate 4114 can be about 2.5micrometers with a range between about 0.5 and 10 micrometers. In thisembodiment, gap distance D1 is the total of the following thickness:thickness of stationary capacitor 4118, the thickness of a firstsacrificial layer for forming gap G, and the thickness of a secondsacrificial layer for forming gap G. Additionally, for example, a gapdistance D2 between isolation bump IP and surface 4116 of substrate 4114can be between about 0.5 and 20 micrometers. In this embodiment, gapdistance D2 is the thickness of the first sacrificial layer.Additionally, for example, a gap distance D3 between planarization oxidePO and surface 4116 of substrate 4114 can be between about 0.5 and 20micrometers. In this embodiment, gap distance D3 is the thickness of thefirst and second sacrificial layers.

[0166] Regarding the embodiment shown in FIG. 41, the unactuatedcapacitance value is about 0.6 picoFarads. The capacitance ratio in thisembodiment is about 13. The higher ratio (greater than 3 times the aboveembodiments assuming silicon oxide as the planarization oxide) andhigher maximum capacitance (greater than 4 times the above embodimentsassuming silicon oxide as the planarization oxide) enabled by having adielectric in the gap provide more control in the circuit and allow theuse of smaller variable capacitors to provide the required function.Higher dielectric constant materials that are compatible with theprocess can also be utilized for the planarization oxide with greatergains in ratio and maximum capacitance.

[0167] Referring to FIG. 42, a cross-sectional side view of anothervariable capacitor, generally designated 4200, having isolation bumpsIP1 and IP2 is illustrated. Variable capacitor 4200 can include amovable component MC having movable actuation electrodes 4202 and 4204positioned on a top and bottom surface 4206 and 4208, respectively.Movable component MC can include movable capacitive electrodes 4210 and4212 positioned on a top and bottom surface 4206 and 4208, respectively.Variable capacitor 4200 can also include a substrate 4214 including atop surface 4216 having a stationary capacitive electrode 4218 depositedthereon.

[0168] Substrate 4214 can include one or more substrate layers,generally designated SL, including a stationary actuation electrode 4220positioned therein. Substrate layers SL can also include a capacitorinterconnect CI for connecting stationary capacitive electrode 4218 to asignal line (not shown). In this embodiment, substrate layers SL includea base substrate layer BSL, a first metal layer M1, a first substratelayer S1, a second metal layer M2, and a second substrate layer S2.

[0169] In this embodiment, one or more sacrificial layers (not shown)can be used during a fabrication process for constructing movablecomponent MC (FIG. 42). The sacrificial layers can subsequently beremoved by a suitable process to form the gap, generally designated G,between movable component MC and substrate 4214. In this embodiment, gapG can extend different distances between movable component MC andsubstrate 4214. For example, a gap distance D1 between movable actuationelectrode 4204 and surface 4216 of substrate 4214 can be about 0.8micrometers. Alternatively, distance D1 can range between about 0.5 and20 micrometers. In this embodiment, distance D1 is the thickness of thefirst and second sacrificial layers. Additionally, for example, a gapdistance D2 between isolation bump IP1 and surface 4216 of substrate4214 can be about 0.3 micrometers. Alternatively, distance D2 can rangefrom between about 0.2 and 19 micrometers. In this embodiment, gapdistance D2 is the thickness of the first sacrificial layer. For thelargest ratio, the second sacrificial layer should be as thin as isfeasible with suitable thickness control. Additionally, for example, agap distance D3 between movable actuation electrode 4212 and stationaryactuation electrode 4218 can be about 0.5 micrometers. Alternatively,distance D3 can range from between about 0.2 and 20 micrometers. In thisembodiment, gap distance D3 is the thickness of the first and secondsacrificial layers after planarization to level the top of thesacrificial material to the level of the sacrificial material in thearea where there is no portion of electrode 4218. Additionally, forexample, a gap distance D4 between isolation bump IP2 and stationaryactuation electrode 4218 can be about 0.3 micrometers. Alternatively,distance D4 can range between about 0.2 and 19 micrometers. In thisembodiment, gap distance D4 is the thickness of the first sacrificiallayer.

[0170] Regarding the embodiment shown in FIG. 42, the maximumcapacitance value is about 5 picoFarads, and the minimum capacitancevalue is about 2 picoFarads. The capacitance ratio in this embodiment isabout 2.5. In this embodiment, the actuation voltage at the maximumcapacitance is about 15 Volts.

[0171] A variable capacitor according to one embodiment can include arotatable movable component attached to one or more torsional beams forproviding resistance to the rotational motion. The movable component canbe attached to the torsional beam such that the movable component hastwo “free” ends for rotating about the torsional beam. One or moremovable actuation electrodes can be disposed on one end of the movablecomponent. Additionally, one or more movable capacitive electrodes canbe disposed on an opposing end of the movable component such that theattachment of the torsional beam is between the movable capacitiveelectrodes and the movable actuation electrodes. When the movableactuation electrodes are actuated, the movable actuation electrode cancause its corresponding end of the movable component to move downwardand rotate the movable component about the torsional beams.Additionally, when the movable actuation electrodes are actuated, theopposing end of the movable component can move upward to displace themovable capacitive electrode from an associated stationary capacitiveelectrode for changing the capacitance of the variable capacitor.

[0172]FIGS. 43-45 illustrate different views of a variable capacitor,generally designated 4300, including torsional beams TB1 and TB2.Referring specifically to FIG. 43, a top perspective view of variablecapacitor 4300 is illustrated. Variable capacitor 4300 can include asubstrate 4306 having a pair of spaced-apart pivot posts P1 and P2supporting torsional beams TB1 and TB2, respectively. Torsional beamsTB1 and TB2 can support a movable component MC for rotational movementof opposing ends of movable component MC about a pivot axis (generallydesignated with a broken line 4308 extending from a side of movablecomponent MC). Torsional beams TB1 and TB2 can also provide resistanceto the rotational movement of movable component MC. The center supportof these torsional beams enables robust fabrication and operation oftorsional variable capacitors using movable component MC layers withcompressive intrinsic stresses.

[0173] Torsional beams TB1 and TB2 can provide vertical stiffness tolimit vertical motion of movable component MC with respect to substrate4306. Further, torsional beams TB1 and TB2 can provide torsionalsoftness to ease rotational motion of movable component MC. FIG. 44Aillustrates a cross-sectional side view of one embodiment of variablecapacitor in the direction indicated by lines L1 and L2 (shown in FIG.43). Referring to FIG. 44A, in this embodiment, torsional beams TB1 andTB2 (shown in FIG. 43) can have a rectangular cross-section and a beamof sufficient length to provide flexibility. Alternatively, torsionalbeams TB1 and TB2 can have any suitable cross-section shape, dimension,or length. Additionally, torsional beams TB1 and TB2 can include foldedsprings. Torsional beams TB1 and TB2 can comprise one or more layers ofsilica, alumina, un-doped semiconductors, polymers, and othernon-conductive materials known to those of ordinary skill in the art.

[0174]FIG. 44B illustrates a cross-sectional side view of an alternativeembodiment of variable capacitor 4300. In this embodiment, movablecomponent MC comprises a first portion 4400 and a second portion 4402,wherein second portion 4402 is positioned closer to substrate 4306 thanfirst portion 4400. Therefore, movable actuation electrodes (MAE1 andMAE2) and stationary actuation electrode SAE can be positioned furtherapart than the distance between movable capacitance electrodes (MCE1 andMCE2) and stationary capacitance electrode SCE to its attachment tofirst portion 4400 because movable actuation electrode MAE is positionedon raised first portion 4400. The dual gap can be formed by twodifferent thicknesses of sacrificial layer.

[0175] Referring to FIG. 44C illustrates a cross-sectional side view ofanother alternative embodiment of variable capacitor 4300. Stationaryactuation electrode SAE can be buried in substrate 4306. Thispositioning can increase the distance between stationary actuationelectrode SAE and movable actuation electrodes MAE1 and MAE2 withoutadding the complexity of additional sacrifical layers.

[0176] Substrate 4306 can also include a stationary actuation electrodeSAE and a stationary capacitive electrode SCE formed on a surface 4310thereof. Movable component MC can include movable actuation electrodesMAE1 and MAE2 attached to a top surface 4312 and a bottom surface 4314(shown in FIG. 44), respectively, of movable component MC. Movableactuation electrodes MAE1 and MAE2 can be positioned above stationaryactuation electrode SAE. Movable actuation electrodes MAE1 and MAE2 canbe attached to one terminal of a voltage supply (such as voltage supplyVS shown in FIG. 4) and stationary actuation electrode SAE can beattached to another terminal of the voltage supply for applying apotential difference to actuate variable capacitor 4300. When actuated,movable actuation electrodes MAE1 and MAE2 can move towards stationaryactuation electrode SAE for operatively moving movable component MCalong pivot axis 4308.

[0177] Substrate 4306 can also include a stationary capacitive electrodeSCE attached to surface 4310. Movable component MC can also includemovable capacitive electrodes MCE1 and MCE2 attached to surfaces 4312and 4314, respectively. Capacitive electrodes SCE, MCE1, and MCE2 can beelectrically connected to a signal line (such as signal line SL shown inFIG. 4) for supplying a signal to variable capacitor 4300 from otherelectrical circuitry (not shown). When variable capacitor 4300 isactuated to move movable component MC along pivot axis 4308, movablecapacitive electrodes MCE1 and MCE2 can be moved away from stationarycapacitive electrode SCE to change the capacitance between stationarycapacitive electrode SCE and movable capacitive electrodes MCE1 andMCE2.

[0178] Referring to FIG. 45, a cross-sectional side view of variablecapacitor 4300 in an actuated mode is illustrated. Movable actuationelectrodes MAE1 and MAE2 are positioned closer to stationary actuationelectrode SAE than in an unactuated position as shown in FIGS. 43 and44. Movable capacitive electrodes MCE1 and MCE2 are positioned furtherfrom stationary capacitive electrode SCE than in the unactuated positionshown in FIGS. 43 and 44.

[0179] Variable capacitor 4300 can achieve the specifications shown inTable 5 below. TABLE 5 Summary of Specifications Parameter ValueV_(control) 4.5 V Resonance 2 kHz frequency C_(min) 0.9 pF Capacitanceratio 1:2

[0180] The specifications indicated in Table 5 can be varied by changingthe length of torsional beams T1 and T2 (FIG. 43). A capacitance valueof about 0.26 pF for variable capacitor 4300 can be obtained. Torsionalbeams T1 and T2 can have a length between about 25 and 175 micrometers.FIG. 46 illustrates a graph showing the harmonic behavior for variablecapacitor 4300 (FIGS. 43-45).

[0181] An important parameter effecting resonance frequency isrotational inertia of movable component MC. The rotational inertia ofmovable component MC equals the mass of movable actuation electrodesMAE1 and MAE2 and movable capacitive electrodes SCE1 and SCE2. FIG. 47illustrates a graph showing the frequency response for differentdistances of movable actuation electrodes MAE1 and MAE2 (FIG. 43) andmovable capacitive electrodes SCE1 and SCE2 (FIG. 43) from pivot axis4308 (FIG. 43).

[0182]FIG. 48 illustrates a top view of a schematic diagram of anotherexamplary torsional variable capacitor, generally designated 4800.Variable capacitor 4800 can include a movable capacitor MC having a topsurface 4802. A movable capacitance electrode MCE and a movableactuation electrode MAE can be attached to top surface 4802. Variablecapacitor 4800 can also include pivot posts P1 and P2 and torsionalbeams TB1 and TB2. The dimensions of the components of variablecapacitor 4800 are indicated in micrometers.

[0183] An array of variable capacitor such as variable capacitor 4300shown in FIGS. 43-45 can be arranged in parallel to achieve differentmaximum and minimum capacitances. For example, sixteen variablecapacitors (such as variable capacitor 4300) can be arranged in parallelto achieve a maximum capacitance of 4 pF, a minimum capacitance of 2 pF,and a first resonance mode of 22. kHz. FIG. 49 illustrates a computersimulation model of deformation of a torsional variable capacitor 4900of an array of 16 variable capacitors (such as variable capacitor 4800shown in FIG. 28). The maximum displacement is located near movablecapacitance electrode MCE.

[0184]FIG. 50 illustrates a graph showing the capacitance of a torsionalvariable capacitor (such as variable capacitor 4300 shown in FIG. 43)versus an applied actuation voltage.

[0185]FIG. 51 illustrates a computer simulation model of deformation ofa movable component of a torsional variable capacitor (such as variablecapacitor 4300 shown in FIG. 43) under a stress gradient between +1 and−1 MPa. The corners of movable component have a displacement of nearly 1micrometer.

[0186] A torsional variable capacitor (such as variable capacitor 4300shown in FIG. 43) can include apertures in the movable component fordecreasing the effects of damping. According to one embodiment, theapertures in a torsional variable capacitor can be up to three timeslarger than 5 micrometers.

[0187]FIG. 52 illustrates a computer simulation model of the deformationof a movable component in a torsional variable capacitor (such astorsional variable capacitor 4300 shown in FIG. 43) for an accelerationof 100 g. The displacement of the outer edge of movable capacitanceelectrode 5200 is about −0.09 micrometers. For a 0.3 g acceleration, thedisplacement of the outer edge of movable capacitance electrode 5200 isabout 0.27 nanometers, resulting in a capacitance change of less thanabout 0.05%.

[0188] When a long conductive line is used to connect two or moretorsional variable capacitors (such as torsional variable capacitor 4300shown in FIG. 43) in parallel, the overall RF performance of theconfiguration can be downgraded. In particular, the inductance added bythe connection can lower the self-resonance frequency.

[0189] Table 6 below indicates a summary of specifications for 16torsional variable capacitors (such as variable capacitor 4300 shown inFIG. 44) connected in parallel. TABLE 6 Specification Summary ParameterValue V_(control) 27 V Resonance frequency 22.4 kHz C_(min) 0.12 pF × 16Capacitance ratio maximum 1:2 R(dc) ≈1.5 ohms Vibration sensitivity0.05% for 0.3 g Stress sensitivity negligible Stress gradient −1 μmdeformation (for +/− 1 MPa) Cut-off frequency Un-Damped System

[0190]FIG. 53 illustrate a computer simulation model RF results ofcomputer simulation model for an equivalent circuit of a torsionalvariable capacitor (such as variable 4300 shown in FIG. 43). Referringto FIG. 53, the HFSS electromagnetic, full-wave simulator (availablefrom Ansoft Corporation of Pittsburgh, Pa.) can be used for modeling atorsional capacitor. Referring to FIG. 53, the resonance quality Q andSmith chart, generally designated 5300, of a torsional variablecapacitor (such as variable 4300 shown in FIG. 43) is shown.

[0191] It will be understood that various details of the subject matterdisclosed herein may be changed without departing from the scope of thesubject matter. Furthermore, the foregoing description is for thepurpose of illustration only, and not for the purpose of limitation.

What is claimed is:
 1. A micro-electro-mechanical system (MEMS) variablecapacitor, comprising: (a) first and second actuation electrodes beingspaced apart, and at least one of the actuation electrodes being aboutvertically movable with respect to the other actuation electrode when avoltage is applied across the first and second actuation electrodes; (b)a first capacitive electrode attached to and electrically isolated fromthe first actuation electrode; and (c) a second capacitive electrodeattached to the second actuation electrode and spaced from the firstcapacitive electrode for movement of at least one of the capacitiveelectrodes with respect to the other capacitive electrode uponapplication of voltage across the first and second actuation electrodesto change the capacitance between the first and second capacitiveelectrodes.
 2. A micro-electro-mechanical system (MEMS) variablecapacitor, comprising: (a) a movable component comprising a first andsecond portion attached to a substrate, wherein the first and secondportion are spaced vertically with respect to one another with respectto the substrate; (b) first and second actuation electrodes being spacedapart, wherein the first actuation electrode is attached to a firstportion of the movable component, wherein the second actuation electrodeis attached to the substrate, wherein the first actuation electrode ismovable when a voltage is applied across the first and second actuationelectrodes; (c) a first capacitive electrode attached to the substrate;and (d) a second capacitive electrode attached to second portion of themovable component and spaced from the first capacitive electrode formovement of the first capacitive electrode with respect to the secondcapacitive electrode upon application of voltage across the first andsecond actuation electrodes to change the capacitance between the firstand second capacitive electrodes.
 3. The variable capacitor of claim 2,wherein the movable component moves vertically with respect to thesubstrate.
 4. The variable capacitor of claim 2, wherein the movablecomponent moves rotationally with respect to the substrate.
 5. Amicro-electro-mechanical system (MEMS) variable capacitor, comprising:(a) a movable component; (b) a substrate attached to movable component,wherein the substrate comprises a first and second portion, wherein thefirst and second portion are spaced vertically with respect to oneanother with respect to the movable component; (c) first and secondactuation electrodes, wherein the first actuation electrode is attachedto the movable component, wherein the second actuation electrode isattached to the first portion of the substrate, wherein the firstactuation electrode and movable component are movable when a voltage isapplied across the first and second actuation electrodes; (d) a firstcapacitive electrode attached to the movable component; and (e) a secondcapacitive electrode attached to the second portion of the substrate,wherein the movable component moves of the first capacitive electrodewith respect to the second capacitive electrode upon application ofvoltage across the first and second actuation electrodes to change thecapacitance between the first and second capacitive electrodes.
 6. Amicro-electro-mechanical system (MEMS) variable capacitor, comprising:(a) first and second actuation electrodes being spaced apart, and atleast one of the actuation electrodes being about vertically movablewith respect to the other actuation electrode when a voltage is appliedacross the first and second actuation electrodes; (b) a first capacitiveelectrode attached to and electrically isolated from the first actuationelectrode; and (c) a second capacitive electrode attached to the secondactuation electrode and spaced from the first capacitive electrode formovement of at least one of the capacitive electrodes with respect tothe other capacitive electrode upon application of voltage across thefirst and second actuation electrodes to change the capacitance betweenthe first and second capacitive electrodes.